Гравитация және қашықтық параллелизмі теориясы

Theory of gravity

Teleparallelism (also called teleparallel gravity), was an attempt by Albert Einstein to base a unified theory of electromagnetism and gravity on the mathematical structure of distant parallelism, also referred to as absolute or teleparallelism. In this theory, a spacetime is characterized by a curvature free linear connection in conjunction with a metric tensor field, both defined in terms of a dynamical tetrad field.

There exists a close analogy of geometry of spacetime with the structure of defects in crystal. Dislocations are represented by torsion, disclinations by curvature. These defects are not independent of each other. A dislocation is equivalent to a disclination antidisclination pair, a disclination is equivalent to a string of dislocations. This is the basic reason why Einstein's theory based purely on curvature can be rewritten as a teleparallel theory based only on torsion. There exists, moreover, infinitely many ways of rewriting Einstein's theory, depending on how much of the curvature one wants to reexpress in terms of torsion, the teleparallel theory being merely one specific version of these. A further application of teleparallelism occurs in quantum field theory, namely, two dimensional non linear sigma models with target space on simple geometric manifolds, whose renormalization behavior is controlled by a Ricci flow, which includes torsion. This torsion modifies the Ricci tensor and hence leads to an infrared fixed point for the coupling, on account of teleparallelism ("geometrostasis").